English experts, help me please

Could any of you tell me whether there is a difference between "in 5 mins" and "within 5 mins", please? (For ex., "call me in 5 mins" and "call me within 5 mins" ). I had a disagreement with a friend of mine on it. As far as I knew both of them give the same meaning, but he insisted on the opposite (namely, according to him --> call me in 5 mins=call me 5 mins later; and, call me within 5 mins=you can call me in the period of time starting now.). Is this correct?

Thanks in advance!

I'm afraid your friend is right, handyy.

in 5 minutes = 5 minutes after now (this minute)
within 5 minutes = at any of the 5 minutes after now

Oww, I am surprised -again (I was so sure I was right in this case. ).

Anyway... thank you, dear, you helped so so soooo much!

My answer is just like lilians, nice questions. great topic to argue about :-)